1. Field of the Invention
This invention relates to measuring the channel characteristics of a multi-channel audio system, particularly to methods and apparatuses for measuring such channel characteristics essentially simultaneously in the presence of crosstalk.
2. Description of the Related Art
It is common for tests and measurements to be made on many different types of audio systems to determine whether they are functioning as desired or needed, or simply to characterize the system. Audio systems comprise a wide variety of apparatuses, including without limitation analog audio amplifiers, mixers, recording and playback devices, and telephone channels, and digital audio processors, recording and playback devices, and communication systems. Test and measurement instruments typically apply a known audio stimulus to the input of an audio system, measure the output produced in response to the stimulus, and determine the system characteristics generally by comparing the output to the input. Characteristics of a channel of an audio system that may be determined are, for example, frequency response, phase distortion, and harmonic distortion, but many other characteristics can be determined depending on the circumstances. The linear characteristics can be determined by measuring the linear impulse response of the system, from which the linear characteristics can be derived.
It is well recognized that many audio systems are provided with multiple channels. For example, stereo audio amplifiers are ubiquitous in the music reproduction field. As another example, many different kinds of telephone communications systems, from cables of twisted pairs of wires to optical fibers, provide many distinct communications channels. As yet a further example, audio mixers typically have many channels to accommodate a large number of sound sources to be mixed.
A potential problem with multi-channel audio systems is that undesired signal energy may be coupled from one channel into another. This is known as “crosstalk.” Not only does crosstalk degrade the channel quality, but its presence during testing masks the signal components to be identified. Consequently, the usual approach is to test each channel separately, while the other channels are grounded so that they do not produce any crosstalk in the channel being tested. This makes testing a multi-channel audio system much slower that testing a single channel audio system. Particularly in the case of production testing, this makes the process expensive because it limits the product completion rate.
In audio system test and measurement it is known that one particularly useful type of stimulus to use is a swept frequency signal that starts at a first, low frequency and ends after a short, definite time at a second, high frequency. This stimulus is known as a “chirp.” Using a chirp, the characteristics of an audio channel can be determined quickly over the full spectrum of the ideal channel pass band without being obscured by inter-modulation distortion. One type of chirp that can be used is a linear chirp, whose frequency varies linearly with time. Thus, a linear chirp may be described mathematically as follows:
      x    ⁡          (      t      )        =      sin    ⁡          [              2        ⁢        π        ⁢                                  ⁢                  t          ⁡                      (                                          f                1                            +                                                                    (                                                                  f                        2                                            -                                              f                        1                                                              )                                    ⁢                  t                                T                                      )                              ]      
where t is time;                x(t) is the stimulus signal as a function of time;        f1 is the low, starting frequency, in Hz;        f2 is the high, ending frequency, in Hz; and        T is the total length of the stimulus, in seconds.However, a linear chirp has the drawback that, while useful measurements of some characteristics can be made, harmonic distortion components in the output cannot be distinguished from the linear characteristics, or from one another.        
Another type of chirp that can be used is an exponential, or log-swept sine, chirp, whose frequency vanes exponentially with time. Thus, an exponential chirp may be described mathematically as follows:
      x    ⁡          (      t      )        =      sin    ⁡          [                                    2            ⁢            π            ⁢                                                  ⁢                          f              1                        ⁢            T                                ln            ⁡                          (                                                f                  2                                /                                  f                  1                                            )                                      ⁢                  (                                                    (                                                      f                    2                                                        f                    1                                                  )                                            t                /                T                                      -            1                    )                    ]      
where t is time;                x(t) is the stimulus signal as a function of time;        T is the total length of the chirp, in seconds;        f1 is the low, starting frequency, in Hz; and        f2 is the high, ending frequency, in Hz.The exponential chirp has the important advantage that harmonic distortion components can be distinguished from one another. This is explained, for example, in T. Kite, Measurement of audio equipment with log-swept sine chirps, J. Audio Eng. Soc., vol. 53, p. 107 (2005 January/February).        
More specifically, it can be shown that:
      t    ⁡          (      f      )        =            T              ln        ⁡                  (                                    f              2                        /                          f              1                                )                      ⁢          ln      ⁡              (                  f                      f            1                          )            
where t(f) is the time at which a particular instantaneous frequency f appears in the chirp signal.
If the channel under test generates harmonic distortion such that when the input frequency is f, the harmonic distortion component in the output has a frequency Nf, where N is an integer harmonic, then the group delay of this distortion component is:
      t    ⁡          (      f      )        =            T              ln        ⁡                  (                                    f              2                                      f              1                                )                      ⁢          ln      ⁡              (                  f                      Nf            1                          )            so that each harmonic is offset in time from t(f) by:
      Δ    ⁢                  ⁢          t      N        =      -          T      (                        ln          ⁡                      (            N            )                                    ln          ⁡                      (                                          f                2                                            f                1                                      )                              )      Consequently, the non-linear harmonic distortion characteristics, as well as the linear response characteristics, can be measured using an exponential chirp.
In either case, even the linear response characteristic measurements are made more difficult by crosstalk. So, chirp testing of a multi-channel audio system has ordinarily been done one channel at a time.
In view of the foregoing, it would be desirable to have a way of simultaneously, or essentially simultaneously, testing at least a plurality of the channels of a multiple-channel audio system while measuring all of the ordinary characteristics in the presence of crosstalk, and also measuring crosstalk.